guran, liliana bota, monica-felicia naseem, asim

The aim of this paper is to give some fixed point results in generalized metric spaces in Perov&rsquo / s sense. The generalized metric considered here is the w-distance with a symmetry condition. The operators satisfy a contractive weakly condition of Hardy&ndash / Rogers type. The second part of the paper is devoted to the study of the data depen...

boukarou, aissa guerbati, kaddour zennir, khaled alodhaibi, sultan alkhalaf, salem

Studies of modified Korteweg-de Vries-type equations are of considerable mathematical interest due to the importance of their applications in various branches of mechanics and physics. In this article, using trilinear estimate in Bourgain spaces, we show the local well-posedness of the initial value problem associated with a coupled system consisti...

kozhanov, aleksandr i.

We study the solvability for boundary value problems to some nonlocal second-order integro&ndash / differential equations that degenerate by a selected variable. The possibility of degeneration in the equations under consideration means that the statements of the corresponding boundary value problems have to change depending on the nature of the de...

guran, liliana bota, monica-felicia naseem, asim mitrović, zoran d. de la sen, manuel radenović, stojan

The purpose of this paper is to present some new fixed point results in the generalized metric spaces of Perov&rsquo / s sense under a contractive condition of Hardy&ndash / Rogers type. The data dependence of the fixed point set, the well-posedness of the fixed point problem and the Ulam&ndash / Hyers stability are also studied.

Liu, Yanlin Paicu, Marius Zhang, Ping

In [15], the authors proved that as long as the one-directional derivative of the initial velocity is sufficiently small in some scaling invariant spaces, then the classical Navier-Stokes system has a global unique solution. The goal of this paper is to extend this type of result to the 3-D anisotropic Navier-Stokes system (AN S) with only horizont...

Brogliato, Bernard Tanwani, Aneel

This survey article addresses the class of continuous-time systems where a system modeled by ordinary differential equations (ODEs) is coupled with a static and time-varying set-valued operator in the feedback. Interconnections of this form model certain classes of nonsmooth systems including sweeping processes, differential inclusions with maximal...

Kian, Yavar Yamamoto, Masahiro

We consider the inverse source problem of determining a source term depending on both time and space variable for fractional and classical diffusion equations in a cylindrical domain from boundary measurements. With suitable boundary conditions we prove that some class of source terms which are independent of one space direction, can be reconstruct...

Prieur, Christophe Tarbouriech, Sophie

International audience

colli, pierluigi gilardi, gianni sprekels, jürgen

In this paper, we study the distributed optimal control of a system of three evolutionary equations involving fractional powers of three self-adjoint, monotone, unbounded linear operators having compact resolvents. The system is a generalization of a Cahn&ndash / Hilliard type phase field system modeling tumor growth that has been proposed by Hawki...

Bu, Shangquan Cai, Gang
Published in
Fractional Calculus and Applied Analysis

We study the well-posedness of the fractional degenerate differential equation: Dα (Mu)(t) + cDβ(Mu)(t) = Au(t) + f(t), (0 ≤ t ≤ 2π) on Lebesgue-Bochner spaces Lp(𝕋; X) and periodic Besov spaces Bp,qs $\begin{array}{} B_{p,q}^s \end{array}$ (𝕋; X), where A and M are closed linear operators in a complex Banach space X satisfying D(A) ⊂ D(M), c ∈ ℂ a...